Question

A 7-digit number 345a812 is exactly divisible by 3. Then the number of possible values of a is:

• A. 2
• B. 3
• C. 4
• D. 5

Hint:

Sum of digits of 345a812 must be a multiple of 3.

Answer 1

The Correct Option is B

Step 1: Concept
Divisibility rule for 3.

Step 2: Analysis
A number is divisible by 3 if the sum of its digits is divisible by 3.

Step 3: Calculation
Sum = $3+4+5+a+8+1+2 = 23 + a$.
Possible values for $a$ (0-9) to make $(23+a)$ divisible by 3:
If $a=1, \text{sum}=24$; if $a=4, \text{sum}=27$; if $a=7, \text{sum}=30$.

Step 4: Conclusion
There are 3 possible values for $a$ (1, 4, 7). Final Answer: (B)